I was doing beta elimination with 0.1M of Ba(OH)2 at 37 and 55 degrees for 2 and 24 h. In all conditions I lost more than half of the peptides. How can this be explained?
Your peptide might be lost to precipitation, especially if it has high pKa. Note that successful beta-elimination will increase pKa, through loss of carboxylate from acidic residues. You may be able to release peptide into solution with an acidic workup. I'd recommend HOAc for this strategy.
Also, alkali hydrolyzes peptide bonds, irreversibly destroying the peptide. To minimize this side reaction, try using lower temperatures.